Optimization Design and Analysis of Systematic LT codes over AWGN Channel

TL;DR

This paper introduces an optimized encoding scheme for systematic LT codes over AWGN channels, employing a novel linear programming approach to improve BER performance and analyzing their theoretical bounds.

Contribution

It proposes a new linear programming method to optimize degree distributions of SLT codes, enhancing their error performance over AWGN channels.

Findings

Optimized degree distributions improve BER performance.

Derived closed-form expressions for lower bounds.

Simulation confirms the effectiveness of the proposed method.

Abstract

In this paper, we study systematic Luby Transform (SLT) codes over additive white Gaussian noise (AWGN) channel. We introduce the encoding scheme of SLT codes and give the bipartite graph for iterative belief propagation (BP) decoding algorithm. Similar to low-density parity-check codes, Gaussian approximation (GA) is applied to yield asymptotic performance of SLT codes. Recent work about SLT codes has been focused on providing better encoding and decoding algorithms and design of degree distributions. In our work, we propose a novel linear programming method to optimize the degree distribution. Simulation results show that the proposed distributions can provide better bit-error-ratio (BER) performance. Moreover, we analyze the lower bound of SLT codes and offer closed form expressions.